Question

Calculate the theoretical yield of aspirin to be obtained in this experiment, starting with \(2.0 \mathrm{g}\) of salicylic acid and \(5.0 \mathrm{mL}\) of acctic anhydride (density = \(1.08 \mathrm{g} / \mathrm{mL}\) ). _____ \(g\)

Short answer

The theoretical yield of aspirin can be calculated using the following steps: 1. Moles of salicylic acid = \(\frac{2.0 \ \mathrm{g}}{138.12 \ \mathrm{g/mol}}\) 2. Mass of acetic anhydride = 5 mL × 1.08 g/mL = 5.4 g, and moles of acetic anhydride = \(\frac{5.4 \ \mathrm{g}}{102.09 \ \mathrm{g/mol}}\) 3. Determine the limiting reactant using the mole ratio and stoichiometry of the reaction. 4. Calculate the theoretical yield of aspirin using the moles of the limiting reactant and the molar mass of aspirin (180.16 g/mol): Theoretical yield of aspirin = moles of limiting reactant × 180.16 g/mol.

Step-by-step solution

Convert to moles

First, we need to convert the mass of salicylic acid and the volume of acetic anhydride to moles. The molar mass of salicylic acid (C₇H₆O₃) is 138.12 g/mol, and the density of acetic anhydride is 1.08 g/mL. So, we can calculate the moles as follows: Moles of salicylic acid = \(\frac{2.0 \ \mathrm{g}}{138.12 \ \mathrm{g/mol}}\) For acetic anhydride (C₄H₆O₃), we first convert the volume to mass using the density, then calculate the moles using its molar mass (102.09 g/mol): Mass of acetic anhydride = 5 mL × 1.08 g/mL = 5.4 g Moles of acetic anhydride = \(\frac{5.4 \ \mathrm{g}}{102.09 \ \mathrm{g/mol}}\)

Determine the limiting reactant

The balanced chemical equation for the synthesis of aspirin is: C₇H₆O₃ (salicylic acid) + C₄H₆O₃ (acetic anhydride) → C₉H₈O₄ (aspirin) + CH₃COOH (acetic acid) From the stoichiometry of the reaction, we need 1 mole of salicylic acid for every 1 mole of acetic anhydride to react completely. To find the limiting reactant, we will compare the mole ratio of the reactants: Mole ratio = \(\frac{\text{Moles of salicylic acid}}{\text{Moles of acetic anhydride}}\) If the mole ratio is less than 1, the salicylic acid is the limiting reactant. If the mole ratio is greater than 1, the acetic anhydride is the limiting reactant. If the mole ratio is 1, both reactants are in stoichiometric proportion, and neither is limiting.

Calculate the theoretical yield

Once we've determined the limiting reactant, we can calculate the theoretical yield of aspirin using the stoichiometry of the balanced equation. For every mole of limiting reactant, we will obtain 1 mole of aspirin (C₉H₈O₄). The molar mass of aspirin is 180.16 g/mol. Theoretical yield of aspirin = moles of limiting reactant × 180.16 g/mol Finally, we multiply the moles of limiting reactant by the molar mass of aspirin to obtain the theoretical yield in grams.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions.
In essence, it's a method of quantifying the amount of products that should form from a given quantity of reactants under the law of conservation of mass. This concept is pivotal when you're entering the world of chemical reactions because it allows you to predict the outcomes of reactions in a measurable and calculable way.

For example, consider the reaction for the creation of aspirin; using stoichiometry, you can understand how to balance the equation and find out how many moles of each reactant are needed to produce a certain amount of product. It's akin to a recipe; if you know you need two eggs per cake and you have ten eggs, you can calculate that you'll be able to bake five cakes—stoichiometry does the same for chemical reactions.

Limiting Reactant

The limiting reactant in a chemical reaction is the substance that is totally consumed when the chemical reaction is complete.
When it runs out, the reaction stops, and no further products can form, even if other reactants remain. Identifying the limiting reactant is crucial because it determines the maximum amount of product that can be formed from the given amounts of reactants.

To identify the limiting reactant, one should calculate and compare the moles of all reactants. The one with the fewest moles per stoichiometric requirement is the limiting reactant. As stated in our exercise solution, the comparison of the mole ratio of salicylic acid to acetic anhydride validates which reactant limits the reaction. Understanding this concept is like knowing you can't make more sandwiches than the number of slices of bread you have left; the bread limits your sandwich-making potential.

Molar Mass

Molar mass, the weight of one mole of a substance, is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. The unit for molar mass is grams per mole (g/mol). It's an essential concept for converting between mass, moles, and number of particles.

Understanding the molar mass allows us to convert the mass of a substance to the number of moles and vice versa as seen in the exercise provided. For example, to determine how many moles of salicylic acid are present in a 2.0 gram sample, the calculation would involve dividing by its molar mass, thus determining the amount of substance available to react. Think of molar mass as a conversion factor that translates between the micro world of atoms and molecules to the macro world we measure in grams and liters.